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Translates of ratio...
Translates of rational points along expanding closed horocycles on the modular surface
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- Burrin, Claire (author)
- Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA.;Swiss Fed Inst Technol, Dept Math, CH-8092 Zurich, Switzerland
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- Shapira, Uri (author)
- Technion, Dept Math, Haifa, Israel
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- Yu, Shucheng (author)
- Uppsala universitet,Matematiska institutionen,Technion, Dept Math, Haifa, Israel
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Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA;Swiss Fed Inst Technol, Dept Math, CH-8092 Zurich, Switzerland Technion, Dept Math, Haifa, Israel (creator_code:org_t)
- 2021-09-20
- 2022
- English.
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In: Mathematische Annalen. - : Springer Berlin/Heidelberg. - 0025-5831 .- 1432-1807. ; 382:1-2, s. 655-717
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Abstract
Subject headings
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- We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface. Using spectral methods we confirm equidistribution of these sample points for any translate when the sequence of horocycles expands within a certain polynomial range. We show that the equidistribution fails for generic translates and a slightly faster expanding rate. We also prove both equidistribution and non-equidistribution results by obtaining explicit limiting measures while allowing the sequence of horocycles to expand arbitrarily fast. Similar results are also obtained for translates of primitive rational points.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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